Why is the total distance traveled by a mass traveling in a circle of radius R during n revolutions, 2piRn?
C = 2pir units / rev = circumference.
d = 2pir units / rev * n rev = Total
distance traveled.
Now let's use real numbers:
r = 5m.
n = 10revs.
C = 2pir = 6.28 * 5m = 31.4m/rev.
d = 2pirn = 31.4m/rev * 10revs = 314m.
To understand why the total distance traveled by a mass traveling in a circle of radius R during n revolutions is 2πRn, we need to break it down.
1. Circumference of a Circle:
The circumference of a circle is given by the formula C = 2πR, where R is the radius of the circle. This formula represents the distance around the circle once.
2. Distance Covered in One Revolution:
Since one revolution means completing a full circle, the distance covered during one revolution is equal to the circumference of the circle, which is 2πR.
3. Distance Covered in n Revolutions:
To find the total distance covered during n revolutions, we need to multiply the distance covered in one revolution (2πR) by the number of revolutions (n).
Therefore, the total distance traveled by a mass traveling in a circle of radius R during n revolutions is given by the formula: Distance = 2πRn.
So, by multiplying the circumference of the circle (2πR) by the number of revolutions (n), we get the total distance traveled.